If f(x) = $$\dfrac{ (4x + 3)}{(6x – 4)}$$, x ≠ ($$\dfrac{2}{3}$$) show that fof(x) = x, for all x ≠ ($$\dfrac{2}{3}$$). What is the inverse of f?

Asked by Aaryan | 1 year ago |  175

##### Solution :-

It is given that f(x) = $$\dfrac{ (4x + 3)} {(6x – 4)}$$, x ≠ $$\dfrac{2}{3}$$

Now we have to show fof(x) = x

(fof)(x) = f (f(x))

=$$\dfrac{ (4x+ 3)}{(6x – 4)}$$

$$\dfrac{34x}{34}$$

= x

Therefore, fof(x) = x for all x ≠ $$\dfrac{2}{3}$$

= fof = 1

Hence, the given function f is invertible and the inverse of f is f itself

Answered by Aaryan | 1 year ago

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